I'd say Lydia would beat Aela any day of the weak. However, Aela, Farkas, Skjor, and Vilkas vs. Lydia and three other housecarls, it wouldn't even be a question (even though each Housecarl could probably beat any given Companion in single combat). The companions fight as a team.
If Aela tried to turn into a werewolf before the fight, Lydia would know what she's up against, shield bash Aela into submission, and kill her without much risk to herself.
If Aela tried to take Lydia out with a bow, it depends on whether she can get around Lydia's shield, but too many will be thwarted, Lydia would close the distance, and win.
If Aela tried to turn into a werewolf to try to pull out a victory, Lydia would slay her while she's still writhing in the agony of the transformation, and the claws would never see action - seriously, transforming into a werewolf in the middle of a fight is suicide (I suggest NOT trying it, unless you're eager to reload or lose a DiD character)